Applied Mathematics Commons^™

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

Evaporation Of A Sessile Droplet On A Slope, Mitch Timm

Dissertations, Master's Theses and Master's Reports

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from a purely diffusive transport of the liquid vapor and that the contact line is a pinned circle. For the purposes of our analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the …

Operational Research: Multi-Period Stowage Policies Within A Multi-Zone Storage Framework., Joseph Loeffler

All Graduate Theses, Dissertations, and Other Capstone Projects

This paper will be extending the single period stowage decision model presented by [Yuan, 2017] into a multi-period stowage decision model. The stowage decision determines how incoming items are distributed and stored across multiple storage zones. The amount of items that can be picked in any given storage zone is finite within a single time period. With this constraint, this research attempts to optimize how items are stored across many zones to meet uncertain demand requirements. A simulation study will be performed to compare the stowage policies given by [Yuan, 2017] to see how well they generalize to multi-period model. …

The Vendor In A Retail Setting: A Survey, Jesse Laporte

All Graduate Theses, Dissertations, and Other Capstone Projects

We consider the problem of managing nonperishable inventory as a vendor in a grocer setting. To manage inventory effectively, we must meet the demand of our customers as closely as we can. Too much inventory results in holding costs and ties up a large amount of capital and too little inventory results in lost sales or substitution. It is typical in a retail setting for the vendor to have access to past ordering data, but this data is only representative of the demand when we have sufficient inventory. Otherwise, the demand exceeds the inventory on hand and we lose, in …

Computational Investigation Of Energetic Materials: Influence Of Intramolecular And Intermolecular Interactions On Sensitivity, Ashley Lauren Shoaf

Chemistry & Biochemistry Theses & Dissertations

The development of novel high energy density materials (HEDMs) with superior energetic properties depends on characterizing how and why detonation occurs. Detonation is highly energetic and a nearly instantaneous process, making experimental studies challenging; thus, computational modeling through density functional theory (DFT) and molecular dynamics (MD) can be used to propose weakened, or activated, bonds that break to initiate explosive decomposition, termed trigger bonds. Bond activation is characterized by the Wiberg bond index (WBI), a measure of interatomic electron density. Trigger bonds in HEDMs are commonly found in explosophores, functional groups that contribute to energetic potential such as X-NO_{2 …}

Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans

Williams Honors College, Honors Research Projects

The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and …

Pseudo-Companion Matrices For Polynomial Systems, Melinda Kleczynski

Dissertations, Master's Theses and Master's Reports

Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.

High Accuracy Methods And Regularization Techniques For Fluid Flows And Fluid-Fluid Interaction, Mustafa Aggul

Dissertations, Master's Theses and Master's Reports

This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all …

High-Order Integral Equation Methods For Quasi-Magnetostatic And Corrosion-Related Field Analysis With Maritime Applications, Robert Pfeiffer

Theses and Dissertations--Electrical and Computer Engineering

This dissertation presents techniques for high-order simulation of electromagnetic fields, particularly for problems involving ships with ferromagnetic hulls and active corrosion-protection systems.

A set of numerically constrained hexahedral basis functions for volume integral equation discretization is presented in a method-of-moments context. Test simulations demonstrate the accuracy achievable with these functions as well as the improvement brought about in system conditioning when compared to other basis sets.

A general method for converting between a locally-corrected Nyström discretization of an integral equation and a method-of-moments discretization is presented next. Several problems involving conducting and magnetic-conducting materials are solved to verify the accuracy …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

An Application Of M-Matrices To Preserve Bounded Positive Solutions To The Evolution Equations Of Biofilm Models, Richard S. Landry Jr.

LSU New Orleans Theses and Dissertations

In this work, we design a linear, two step implicit finite difference method to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate. Three separate models are analyzed, all of which can be described as systems of partial differential equations (PDE)s with nonlinear diffusion and reaction, where the biological colony grows and decays based on the substrate bioavailability. The systems under investigation are all complex models describing the dynamics of biological films. In view of the difficulties to calculate analytical solutions of the models, we design here a numerical technique …

Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …

Rate Of Convergence For Generalized Szász–Mirakyan Operators In Exponential Weighted Space, Sevilay K. Serenbay, Özge Dalmano˘Glu

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, generalized Szász–Mirakyan operators in exponential weighted space of functions of one variable are introduced. Using a method given by Rempulska and Walczak, some theorems on the degree of approximation are investigated. Furthermore, a numerical example with an illustrative graphic is given to show comparison for the error estimates of the operators.

The Fmx/Fm/1 Queue With Multiple Working Vacation, G. Kannadasan, N. Sathiyamoorthi

Applications and Applied Mathematics: An International Journal (AAM)

This study investigates the batch arrival FM^X/FM/1 queue with multiple working vacation. For this fuzzy queuing model, this research obtains some performance measure of interest such as mean system length, mean system sojourn time, mean busy period for the server and working vacation period. Finally, numerical results are presented to show the effects of system parameters.

Numerical Experiments For Finding Roots Of The Polynomials In Chebyshev Basis, M. S. Solary

Applications and Applied Mathematics: An International Journal (AAM)

Root finding for a function or a polynomial that is smooth on the interval [a; b], but otherwise arbitrary, is done by the following procedure. First, approximate it by a Chebyshev polynomial series. Second, find the zeros of the truncated Chebyshev series. Finding roots of the Chebyshev polynomial is done by eigenvalues of a nXn matrix such as companion or comrade matrices. There are some methods for finding eigenvalues of these matrices such as companion matrix and chasing procedures.We derive another algorithm by second kind of Chebyshev polynomials.We computed the numerical results of these methods for some special and ill-conditioned …

A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.

Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the reliability assessment of a single unit connected to two types of external supporting devices for its operation. Each type of external supporting device has two copies I and II on standby. First order differential difference equations method is used to obtain the explicit expression for the steady state availability, busy period due to failure of type I and II supporting devices of repairmen, steady-state availability and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and …

Analytical Solutions For The Black-Scholes Equation, Jalil Manafian, Mahnaz Paknezhad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the Black-Sholes equation (BS) has been applied successfully with the Cauchy-Euler method and the method of separation of variables and new analytical solutions have been found. The linear partial differential equation (PDE) transformed to linear ordinary differential equation (ODE) as well. We acquired three types of solutions including hyperbolic, trigonometric and rational solutions. Descriptions of these methods are given and the obtained results reveal that three methods are tools for exploring partial differential models.

Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general …

Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we proposed hybrid conjugate gradient method using the convex combination of FR and PRP conjugate gradient methods for solving Large-scale symmetric nonlinear equations via Andrei approach with nonmonotone line search. Logical formula for obtaining the convex parameter using Newton and our proposed directions was also proposed. Under appropriate conditions global convergence was established. Reported numerical results show that the proposed method is very promising.

Analytical Solution For Determination The Control Parameter In The Inverse Parabolic Equation Using Ham, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the homotopy analysis method (HAM) for obtaining the analytical solution of the inverse parabolic problem and computing the unknown time-dependent parameter is introduced. The series solution is developed and the recurrence relations are given explicitly. Special attention is given to satisfy the convergence of the proposed method. A comparison of HAM with the variational iteration method is made. In the HAM, we use the auxiliary parameter ~ to control with a simple way in the convergence region of the solution series. Applying this method with several

Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson

Dissertations

In the numerical solution of partial differential equations (PDEs), there is a need for solving large scale problems. The Radial Basis Function Differential Quadrature (RBFDQ) method and local RBF-DQ method are applied for the solutions of boundary value problems in annular domains governed by the Poisson equation, inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. By choosing the collocation points properly, linear systems can be obtained so that the coefficient matrices have block circulant structures. The resulting systems can be efficiently solved using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). For the local RBFDQ method, the …

Stochastic Analysis Of A Mammalian Circadian Clock Model: Small Protein Number Effects, David W. Morgens, Blerta Shtylla

Spora: A Journal of Biomathematics

The circadian clock, responsible for coordinating organism function with daily and seasonal changes in the day-night cycle, is controlled by a complex protein network that constitutes a robust biochemical oscillator. Deterministic ordinary differential equation models have been used extensively to model the behavior of these central clocks. However, due to the small number of proteins involved in the circadian oscillations, mathematical models that track stochastic variations in the numbers of clock proteins may reveal more complex and biologically relevant behaviors. In this paper, we compare the response of a robust yet detailed deterministic model for the mammalian circadian clock with …

Examining The Electrical Excitation, Calcium Signaling, And Mechanical Contraction Cycle In A Heart Cell, Kristen Deetz, Nygel Foster, Darius Leftwich, Chad Meyer, Shalin Patel, Carlos Barajas, Matthias K. Gobbert, Zana Coulibaly

Spora: A Journal of Biomathematics

As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitation-contraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical …

Heads And Tails, Julie Simons

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Cellular Automaton Modeling Approach To Chestnut Blight Canker Development, Samuel Iselin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Method For Sensitivity Analysis And Parameter Estimation Applied To A Large Reaction-Diffusion Model Of Cell Polarization, Marissa Renardy, Tau-Mu Yi, Dongbin Xiu, Ching-Shan Chou

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analysis And Implementation Of Numerical Methods For Solving Ordinary Differential Equations, Muhammad Sohel Rana

Masters Theses & Specialist Projects

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis consists of an investigation of various categories of numerical methods for the solution of ordinary differential equations including the numerical solution of ordinary differential equations from a number of practical fields such as equations arising in population dynamics and astrophysics. It …